We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for non-Hermitian quantum systems. Initially we identify a point transformation as a map from an exactly solvable time-independent system to an explicitly time-dependent non-Hermitian Hamiltonian system. Subsequently we employ the point transformation to construct the non-Hermitian time-dependent invariant for the latter system. Exploiting the fact that this invariant is pseudo-Hermitian, we construct a corresponding Dyson map as the adjoint action from a non-Hermitian to a Hermitian invariant, thus obtaining solutions to the time-dependent Dyson and time-dependent quasi-Hermiticity equation together with solutions to the corresponding time-dependent Schrödinger equation.

我们证明了复点变换可用于构造非厄米量子系统的非厄米第一积分、时间相​​关戴森图和度量算子。最初，我们将点变换识别为从完全可解的时间无关系统到显式时间相关的非厄米哈密顿系统的映射。随后，我们采用点变换为后一个系统构造非厄米时间相关的不变量。利用这个不变量是伪厄米不变量的事实，我们构造了相应的戴森映射作为从非厄米不变量到厄米不变量的伴随作用，从而获得了时间依赖戴森和时间依赖拟厄米方程的解相应的时间相关薛定谔方程的解。